structure technical advance - stanford university...structure technical advance flexible fitting of...
TRANSCRIPT
Structure
Technical Advance
Flexible Fitting of Atomic Structures intoElectron Microscopy Maps UsingMolecular DynamicsLeonardo G. Trabuco,1,2,6 Elizabeth Villa,1,2,6 Kakoli Mitra,3,7 Joachim Frank,3,4,8 and Klaus Schulten1,5,*1Beckman Institute2Center for Biophysics and Computational Biology
University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA3Howard Hughes Medical Institute, Health Research Incorporated, Wadsworth Center, Empire State Plaza, Albany, NY 12201, USA4Department of Biomedical Sciences, State University of New York, Albany, NY 12222, USA5Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA6These authors contributed equally to this work.7Present address: Skirball Institute, New York University, New York, NY 10016, USA.8Present address: Howard Hughes Medical Institute, Department of Biochemistry and Molecular Biophysics and Department of Biology,
Columbia University, New York, NY 10032, USA.
*Correspondence: [email protected] 10.1016/j.str.2008.03.005
SUMMARY
A novel method to flexibly fit atomic structures intoelectron microscopy (EM) maps using moleculardynamics simulations is presented. The simulationsincorporate the EM data as an external potentialadded to the molecular dynamics force field, allow-ing all internal features present in the EM map to beused in the fitting process, while the model remainsfully flexible and stereochemically correct. The mo-lecular dynamics flexible fitting (MDFF) method isvalidated for available crystal structures of proteinand RNA in different conformations; measures to as-sess and monitor the fitting process are introduced.The MDFF method is then used to obtain high-reso-lution structures of the E. coli ribosome in differentfunctional states imaged by cryo-EM.
INTRODUCTION
A key to understanding how biological systems work is to look at
their structures captured in their various functional states. Exper-
imental techniques reveal different levels of macromolecular
structure: high-resolution techniques such as X-ray crystallogra-
phy furnish atomic detail, but structures obtained are often in
functionally undefined states; techniques such as cryo-electron
microscopy (cryo-EM) image systems captured in different func-
tional states, albeit at lower resolution (Saibil, 2000). Computa-
tional techniques can help bridge the resolution gap by adapting
high-resolution crystallographic structures to EM maps, thus
providing atomic detail of the system in different functional
states. These techniques can also be used to analyze the phys-
ical and dynamical properties of the resulting structures, reveal-
ing astonishing views of cellular processes.
Until a few years ago, typical resolutions for EM maps of bio-
molecules were 15–30 A, and high-resolution crystal structures
were often available only for domains of a biomolecular complex
Structure
(Frank, 2002; Rossmann, 2000). This led to the development of
so-called rigid-body docking techniques that fit atomic struc-
tures into density maps keeping the high-resolution structure
rigid, usually by performing an exhaustive search over all rota-
tional and translational degrees of freedom in real or reciprocal
space, guided by some choice of similarity measure. Rigid-
body docking has reached maturity, permitting today the inde-
pendent docking of parts of the assembly into a map, thus pro-
ducing a jigsaw structure of the macromolecular complex as
a whole. The main limitation of this class of methods is that neither
the interaction between the docked subunits nor the difference in
conformation between the structures of the domains in crystal
form and in the complex can be determined. A comprehensive
review of the available rigid-body docking methods can be found
in Wriggers and Chacon (2001).
Recent improvements in the resolution of cryo-EM structures
motivated the development of methods to flexibly fit atomic
structures into density maps. In these methods, many degrees
of freedom are considered in the fit, allowing the atomic struc-
tures to undergo conformational changes that improve their
correspondence to the EM map. Various approaches to flexible
fitting have recently been employed and have provided insight
into the structural mechanisms of a number of biomolecular
processes. One of the first attempts to introduce flexibility in
the fitting process, still in use today, consists in dividing a macro-
molecule into ‘‘rigid bodies’’ and fitting them independently (e.g.,
Volkmann et al., 2000). Refinement techniques can then be ap-
plied to the resulting structure, such as the real-space refinement
originally developed for X-ray crystallography (Chapman, 1995;
Chen et al., 2001). Other approaches include the use of so-called
vector quantization, where a reduced representation is derived
from both the atomic structure and the EM map and used as
constraints in a molecular mechanics refinement (Wriggers
et al., 2000; Wriggers and Birmanns, 2001); the use of a linear
combination of low-frequency normal modes to deform the
atomic structure, applying minimization techniques to maximize
the correlation coefficient between atomic structure and EM
map (Tama et al., 2004; Suhre et al., 2006); the combination of
comparative modeling, based on alternative alignments and
16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 673
Structure
Molecular Dynamics Flexible Fitting
loop conformations, and structure refinement (Topf et al., 2006);
the generation of deformed structures based on the variability
exhibited by the protein domains of a superfamily and subse-
quent selection of the best fit based on the cross-correlation co-
efficient (Velazquez-Muriel et al., 2006); the use of a combination
of restraints imposed by the EM map and a deformable elastic
network (Schroder et al., 2007); the use of Monte Carlo simula-
tions with constraints derived from a rigidity analysis (Jolley
et al., 2008); and a hierarchical approach consisting of docking
the structure as one or more rigid bodies with a Monte Carlo
search, followed by two refinement steps based on minimization
of a scoring function and simulated annealing (Topf et al., 2008).
Li and Frank (2007) recently correlated an ensemble of conforma-
tions from equilibrium molecular dynamics (MD) simulations with
cryo-EM data, suggesting that a cryo-EM map can be interpreted
as a conformational average and that using MD to flexibly fit
structures into EM maps should yield structures representative
of the conformational ensemble represented by the EM map, par-
ticularly when combined with an enhanced sampling technique.
We suggest here a novel method to perform MD simulations to
flexibly fit atomic structures into EM maps, with the MD simula-
tion incorporating EM data through an external potential. Forces
proportional to the density gradient of the EM map are added in
the MD simulation of the atomic structure, effectively biasing the
system toward the region of conformational space of interest,
i.e., one that is consistent with the density distribution of the
EM map. Since large forces are applied and simulations pres-
ently are performed in vacuo, harmonic restraints must be
applied to keep secondary structure elements intact, thus
preventing structural distortions and ‘‘overfitting.’’ The molecular
dynamics flexible fitting (MDFF) method presented brings
together several of the most desirable features of existing
methods. First, MDFF takes into account all information con-
tained in the map by avoiding the use of reduced representations
or global measures of similarity to drive the fitting. Since the
external potential is applied locally, it is possible to fit some com-
ponents of a macromolecular assembly even when the structure
of the remaining components is not available. Moreover, the
degree of success of the MDFF method is expected to be inde-
pendent of system size, which is an advantage over the use of
optimization or Monte Carlo-based approaches that employ
global-optimization criteria, where an increase in system size
decreases the likelihood of successful transitions.
The two methods that MDFF is based on, namely, conven-
tional MD simulation and 3D cryo-EM single-particle reconstruc-
tion, are introduced in the online Supplemental Data (see Molec-
ular Dynamics Situations and 3D EM Reconstructions) that
accompanies this article for the nonexpert reader. In the follow-
ing, we describe how the MDFF method incorporates EM data
into MD simulations and how it applies restraints to preserve
the integrity of structural elements. We demonstrate MDFF by
fittings into noise-free, simulated maps created from atomic
structures. Finally, as an example application of MDFF, we fit
atomic structures into cryo-EM maps of the E. coli ribosome at
different resolutions.
MD Simulation with an EM-Derived External PotentialIn the MDFF method, an external potential derived from the EM
map is introduced into an MD simulation to steer the atoms into
674 Structure 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights r
high-density regions. The stereochemical quality of the structure
is preserved by the MD force field and also through harmonic
restraints applied to enforce the integrity of secondary structure.
The method, therefore, adds two extra terms to the potential
energy function of an MD simulation
Utotal = UMD + UEM + USS; (1)
where UMD is the conventional MD potential energy function
(Supplemental Data, see Molecular Dynamics Situations), UEM
corresponds to a potential derived from the EM data, and USS
is a potential that aims to preserve the secondary structure of
protein and nucleic acids. We now describe the latter two terms.
The data provided by cryo-EM reconstructions represent the
Coulomb potential of the macromolecule (Supplemental Data,
see 3D EM Reconstructions); the dependence of this potential
on the atomic number of the composing atoms makes it roughly
proportional to the mass density of the macromolecule. It is then
sensible to define a potential so that when the atomic structure is
placed in it, the atoms are driven through application of forces
into high-density areas and away from low-density areas. This
potential can be defined on a grid, thus preserving all the infor-
mation contained in the EM density map. The potential energy
function corresponding to this map is
UEMðRÞ=X
j
wjVEMðrjÞ; (2)
where R collects all atom coordinates and
VEMðrÞ= { xh1� FðrÞ�Fthr
Fmax�Fthr
iif FðrÞRFthr ;
x if FðrÞ<Fthr:
(3)
Here F(r) is the Coulomb potential revealed by cryo-EM, Fmax is
the maximum value of all voxels in the EM map, x is an arbitrary
scaling factor (x > 0) discussed below, Fthr is a threshold value
used to disregard data not corresponding to the biomolecule,
i.e., solvent density, wi is a weight that can be varied according
to the type of atom placed in this potential, typically set to the
atomic mass, and rj is the position of atom j. The global minimum
of UEM alone corresponds to all atoms collapsed on the density
maximum; however, the other two terms in Equation 1 counter-
balance this effect, preserving physically sound structures.
The threshold value Fthr is selected in accordance with the
density histogram of the EM map, which reveals two peaks of
different density (Frank, 2006); an example is shown in Figure 1A.
The first and higher peak corresponds to solvent density,
whereas the second, broader peak corresponds to protein and
nucleic acid density. The density histogram thus suggests a nat-
ural threshold value at the minimum between the two density
peaks; clamping all values below this threshold removes the sol-
vent contribution and yields a flat potential in the solvent regions.
For cases where the solvent and biomolecule peaks are not well
resolved, the average, which generally lies at the solvent peak, is
chosen as the threshold, thus removing much of the undesired
density while conservatively avoiding loss of macromolecular
density information, as portrayed in Figure 1C.
The force applied to an atom inside the potential defined by
Equation 3 is
eserved
Structure
Molecular Dynamics Flexible Fitting
Figure 1. Reconstruction of the E. coli Ribosome from Cryo-EM Data at �12.8 A Resolution
(A) A density histogram shows two distinct peaks pertaining to the solvent and macromolecule; (B) 2D slice of the density; (C) 2D slice of the density after clamping
values below the average, thus homogenizing the density corresponding to the solvent surrounding the macromolecule and the bulk solvent. Unpublished data
from K.M., L.G.T., E.V., A. Zavialov, M. Ehrenberg, K.S., and J.F.
fEMi = � v
vri
UEMðRÞ= �wi
v
vri
VEMðriÞ (4)
where UEM is the potential energy function introduced in Equa-
tions 2 and 3. fEMi can thus be tuned via the scaling factor x, which
is the same for all atoms, and the weight wi, which can be defined
on a per-atom basis. The external forces fEMi are applied in MDFF
using grid-steered molecular dynamics, an extension of the SMD
method (Isralewitz et al., 2001; Sotomayor and Schulten, 2007)
that allows an arbitrary steering potential to be defined on a grid
(Wells et al., 2007). The force applied to each atom i depends
only on the gradient of the potential derived from the EM density
map at position ri; thus, the fitting in MDFF is performed locally.
In order to preserve the stereochemical quality of the structure
and prevent overfitting in MDFF, harmonic restraints are applied
to a set of internal coordinates relevant to the secondary struc-
ture of the macromolecule in its initial conformation—in many
cases, the crystal structure. For protein structures, harmonic
restraints are applied to f and c dihedral angles of amino-acid
residues in helices and b strands. For nucleic acids, the software
package RNAView (Yang et al., 2003) is used to identify and clas-
sify base pairs. The following base pair types, which were ob-
served to preserve the secondary structure of RNA in simulation
when restrained, are selected: W/W, W/H, W/S, H/H, H/S, and
stacked (W , Watson-Crick edge; H, Hoogsteen edge; S, sugar
edge; see Figure 2A). For these base pairs, harmonic restraints
are applied to the seven dihedral angles (a, b, g, d, 3, z, and c)
and two interatomic distances (d1 and d2) depicted in Figure 2B,
the latter to preserve the planarity of the base pair. Thus, an extra
term introducing secondary structure harmonic restraints is
added to the potential energy function, namely
USS =X
m
kmðXm � X0mÞ
2; (5)
where the restraints Xm stand for protein dihedral angles f and c,
RNA dihedral angles a, b, g, d, 3, z, and c, and RNA distances d1
and d2. The equilibrium values X0m are generally taken from the
Structure
initial atomic structure but can also be set to ideal values. Addi-
tional restraints can be added, such as codon-anticodon interac-
tions in the ribosome, as discussed below.
The MDFF simulations are performed using NAMD (Phillips
et al., 2005), with the CHARMM27 force field (MacKerell et al.,
1998; Foloppe and MacKerrell, 2000) in vacuo, using a dielectric
constant of 80. A multiple time-stepping integration scheme is
used, calculating bonded interactions every 1 fs and nonbonded
interactions every 2 fs; a cutoff distance of 10 A is used for the
nonbonded interactions. Temperature is maintained at 300 K
using a Langevin thermostat (Brunger et al., 1984) coupled to
all heavy atoms with a damping coefficient of 5 ps�1. Rigid-
body docking performed as the initial step of a fitting protocol
in all examples presented was executed using Situs (Wriggers
et al., 1999).
Flexible-Fitting ProtocolObtaining an optimal fit in MDFF relies on a balance among the
three terms in Equation 1. The first term, UMD, is given by the
choice of standard force field and is here not subject to alter-
ation; the other two terms, UEM and USS, contain parameters
that can be tuned and represent a trade-off: higher forces de-
rived from the EM map (UEM) and lower restraints to secondary
structure (USS) can yield a better fit but can also lead to distor-
tions of the macromolecular structure, a natural concern in flex-
ible fitting methods generally referred to as ‘‘overfitting’’ (Tama
et al., 2004). For UEM, parameters that can be varied are the scal-
ing factor x and atomic weights wi (Equations 2 and 3). The latter
are typically set to the atomic masses while x determines the
range in magnitude of forces applied to the atoms and is usually
set to values around 0.3 kcal/mol, resulting in forces typically on
the order of 10–15 pN (piconewton) per atom (for a carbon atom).
The gradient of the potential derived from the EM density map
can be calculated before the fitting to pick a value of x: high
values can result in high accelerations of atoms, rendering the
simulation unstable. The term USS requires the selection of
16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 675
Structure
Molecular Dynamics Flexible Fitting
spring constants km in Equation 5. Typical values used in MDFF
are km = 200 kcal mol�1 rad�2, or 200 kcal mol�1 A�2 in the
case of RNA distances (300 kcal mol�1 A�2 is a typical spring
constant value for a carbon-carbon bond in the CHARMM27
force field). The choice of these values renders the restrained
secondary structure elements relatively stiff, thus preserving
their structure throughout the simulation.
MDFF can also be performed in multiple steps, varying param-
eters at every step, such that the atomic structure gradually
converges into the EM map. Generally, a step is considered ‘‘fin-
ished’’ when the MD simulation has converged as evaluated by
a goodness measure, e.g., by stabilization of the root-mean-
square deviation (rmsd, given by hðri � hriiÞ2i1=2, where ri is the
position of each atom i); one can also track the correlation be-
tween the trajectory and the EM map, as described later. Natu-
rally, in a last step of MDFF one can switch UEM and USS off and
equilibrate the system subject only to the intrinsic potential UMD.
In a multistep protocol of MDFF, several parameters can be var-
ied besides those mentioned above: (1) Temperature can be ad-
justed to allow the system to overcome energy barriers, exploring
a larger portion of the conformational space in less time, often
done in simulated annealing simulations (Frenkel and Smit,
2002); (2) low-pass filtering the map in a first step can be used
to avoid getting trapped in local minima, followed by use of the
original map—this approach first induces overall domain motions
and refines the structure subsequently on the local scale using the
high-resolution information in the original map; (3) along the same
line, one can initially apply strong harmonic restraints to the sec-
ondary structure and in a subsequent step weaken the restraints
to refine the structure; (4) at any given time, any portion of the
structure may be fixed or restrained to its current position (posi-
tional restraints)—this is useful, e.g., when factors or low-occu-
pancy ligands are introduced for fitting, and the rest of the previ-
ously fitted structure can be fixed or restrained while the ligands
are fitted; (5) one can also delete the density corresponding to
Figure 2. Harmonic Restraints Applied to
Base-Paired RNA Residues
(A) RNA interaction edges for both purines (ade-
nine is shown on the left) and pyrimidines (cytosine
is shown on the right), according to Leontis and
Westhof (1998); (B) dihedral angles, and the two
interatomic distances (dashed lines) to which
harmonic restraints are applied.
parts of the structure, which is useful, for
example, for fitting protein-RNA com-
plexes, as discussed below—the deletion
is done by assuming the current fit is
perfect, creating a simulated map from
the fitted structure as described in the
next section, and using it as a mask to se-
lectively delete a portion of the original EM
map. The new map F’ defining UEM as in
Equation 3 is given by
F0 =
�1� Fsim
maxðFsimÞ
�F (6)
where F is the original EM map and Fsim is the simulated map,
with a maximum voxel value of maxðFsimÞ. Equation 6 results
in potentials with smoother gradients than those obtained from
difference maps.
An important advantage of multistep protocols in MDFF is
evident when fitting protein-RNA complexes into EM maps.
The atomic number of the atoms composing RNA is on average
higher than those composing protein, which may lead to incor-
rect fitting of proteins due to lower-energy minima attracting
them into RNA density. To avoid this problem, the RNA may be
fitted first, followed by deleting the RNA contribution from the
EM map once it is well fitted and by then proceeding with the fit-
ting of the proteins. Alternatively, one may positionally restrain
the RNA structure to prevent the protein from being drawn into
the density the RNA occupies.
Fitting Atomic Structures into Simulated MapsIn the following sections, we demonstrate application of MDFF to
noise-free, simulated EM maps as a means of validation of the
method. We briefly describe how simulated maps are generated
from atomic structures and how we calculate cross-correlation
coefficients between a fitted structure and the EM map. Using ex-
ampleswhereX-raycrystal structuresareavailable in twodifferent
conformations of the same molecule, we apply the method to fit
one conformation into simulated maps generated from the other.
Simulated EM Maps from Atomic Structures
Noise-free simulated EM maps can be created from atomic
structures using the approach described in Stewart et al.
(1993), which assumes that the EM map represents the electro-
static potential of the nuclei. The atomic number of each atom is
interpolated onto a grid, and the resulting 3D density map is sub-
sequently low-pass filtered to the desired resolution. Simulated
maps can be generated from a single structure or from a set of
structures obtained from an MD simulation by averaging maps
created from each frame of the trajectory (see Li and Frank,
676 Structure 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved
Structure
Molecular Dynamics Flexible Fitting
Table 1. Effect of Resolution and Grid Spacing on Flexible Fitting into Noise-Free Simulated Maps using MDFF
System
(PDB Codes) Resolution (A)
Initial
Rmsd (A)
Initial (Local)
Correlation Grid Spacing (A)
Final Mean
Rmsd (A)
Final Mean (Local)
Correlation
ACS/CODH (1OAO) 5.0 14.82 0.677 (0.282) 1.0
2.0
0.75
1.04
0.988 (0.934)
0.986 (0.917)
10.0 14.33 0.778 (0.478) 1.0
2.0
1.25
1.25
0.996 (0.977)
0.996 (0.976)
15.0 13.92 0.817 (0.582) 1.0
2.0
2.01
2.07
0.995 (0.980)
0.995 (0.980)
16S rRNA (2AW7, 2AVY) 5.0 3.60 0.873 (0.611) 1.0
2.0
0.65
0.84
0.992 (0.961)
0.988 (0.939)
10.0 3.57 0.947 (0.812) 1.0
2.0
1.04
1.21
0.996 (0.984)
0.995 (0.976)
15.0 3.56 0.973 (0.901) 1.0
2.0
2.06
2.21
0.992 (0.972)
0.991 (0.965)
For each system, maps were created computationally from a given crystal structure of conformation I and a crystal structure available in an alternative
conformation, II, was fitted into the computed map. The initial backbone rmsd and cross-correlation coefficients correspond to rigid-body docked
structures into computed maps with grid spacing of 2.0 A using Situs with default options. The final mean backbone rmsd values were calculated
from the last 200 ps of 500 ps trajectories. The final mean cross-correlation coefficients were calculated using computed maps generated from the
average of the trajectories. Corresponding local cross-correlation coefficients that consider only the molecular envelope are also shown in parenthesis
(a threshold of 0.2 s was used in these examples).
2007). In the present work, simulated maps are used for three
different purposes: (1) calculate cross-correlation coefficients
between EM maps and atomic structures; (2) delete selected
regions from the experimental EM map based on a fitted atomic
structure; and (3) provide noise-free maps for validation pur-
poses.
Cross-Correlation Coefficients
To quantify the goodness of the fit, a simulated map can be gen-
erated from the fitted atomic structure with the same target
resolution as the EM map. The Pearson’s correlation coefficient
(usually referred to in the EM literature as the cross-correlation
coefficient) between these two data sets, i.e., the simulated (S)
and the experimental (E) 3D maps, can be used as a measure
of similarity between them, and is given by
rSE =hðS� hSiÞ ðE � hEiÞi
sSsE
; (7)
where hSi and hEi correspond to the average voxel values of the
simulated and experimental maps, respectively, and sS and sE
correspond to their standard deviation (Frank, 2006). Note that
the cross-correlation coefficient is normalized, i.e., rSE ˛½�1;1�.All cross-correlation coefficients reported were computed con-
sidering either all voxel values in the density maps (‘‘global corre-
lation’’) or only voxels inside the molecular envelope of the
simulated map (‘‘local correlation’’) (Roseman, 2000), using
a threshold that we report as the number of standard deviations
(s) above the mean of the simulated map. The global correlation,
commonly quoted in the literature, depends sensitively on the
box size arbitrarily selected by the electron microscopist. Larger
boxes result in artificially higher correlation values, leading to
overestimation of the quality of the fit; thus, local correlations
should be preferred.
Validation Using Atomic Structures
in Two Conformations
In order to validate the method and estimate the accuracy of the
fitted structures, we use X-ray structures of molecules available
Structur
in two conformations as test cases. One of the structures is fitted
into noise-free simulated maps of the other at 5, 10, and 15 A
resolutions, after an initial phase of rigid-body docking. Here
we present two examples: acetyl-coenzyme A synthase/carbon
monoxide dehydrogenase (ACS/CODH) (Darnault et al., 2003)
and a 16S rRNA (Schuwirth et al., 2005). Several other examples
are presented in Supplemental Data (see Fitting Atomic Struc-
tures into Simulated Maps).
All simulations used x = 0.3 kcal/mol and km = 200 kcal
mol�1 rad�2 (or 200 kcal mol�1 A�2) for the harmonic restraints
(see Equation 5 and Figure 2B), except for 16S rRNA dihedral re-
straints that were enforced using km = 50 kcal mol�1 rad�2. The
simulations converged in less than 200 ps of simulation but
they were run for 500 ps to improve statistics. Table 1 lists the
correlation coefficients and mean backbone rmsd between the
fitted and target structures, calculated from the last 200 ps of tra-
jectories (a plot of the rmsd through the entire trajectories for
ACS/CODH can be found in the Supplemental Data [see Fitting
Atomic Structures into Simulated Maps]). One can see that the
rmsd decreases with higher resolution. It is important to note
that the simulations result in a representative set of structures
that fit the map. Since fitting atomic structures into low-resolu-
tion data is an indeterminate problem, a representative set of
conformers should be considered when interpreting the data.
The structures presented in this paper serve as an illustration
of one such representative structure for each of the problems
considered. Figure 3 shows the initial and target conformation
for each of the systems, as well as representative structures
from MDFF into 10 A resolution simulated maps.
The final structures closely match the target structures used to
generate the simulated maps; as expected, the match is less pre-
cise for lower resolutions or larger grid spacings. As an example,
at 10 A resolution, which represents a typical resolution for EM
maps today, the final mean backbone rmsd is 1.25 A for ACS/
CODH and 1.04 A for the 16S rRNA. The additional test cases pre-
sented in the Supplemental Data (see Fitting Atomic Structures
e 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 677
Structure
Molecular Dynamics Flexible Fitting
Figure 3. Validation of the MDFF Method Using X-Ray Structures in Two Conformations
(A) Acethyl-CoA synthase/carbon monoxide dehydrogenase; (B) 16S rRNA (only the head is shown for clarity, since it is the only region where the two confor-
mations differ significantly). The target structures and simulated maps are shown in gray, whereas the initial and final fitted structures are shown in green (top) and
colored by backbone rmsd per residue with respect to the target structures (bottom; color scales in A). The final structures correspond to fittings into 10 A sim-
ulated maps generated from the target structures. Movies of the fittings are included in the Supplemental Data (see Movies S1 and S2).
into Simulated Maps) also show that the accuracy obtained by
applying MDFF is comparable to other methods (Jolley et al.,
2008; Topf et al., 2008) and that MDFF can describe a large range
of conformational changes, such as movements around a hinge
and domain shearing. The fact that smaller grid spacings yield
better results suggests that higher-order interpolation schemes
in the grid-based force calculation can improve the fitting; in-
deed, the use of cubic interpolation in the current implementation
of grid-steered molecular dynamics in NAMD (used in the calcu-
lations presented) yielded slightly better results when compared
to linear interpolation (data not shown). The simulated maps pre-
sented in this section differ significantly from EM maps in that
they do not contain noise emerging from the imaging process
and numerical errors due to image processing and reconstruc-
tion, and in that they represent a single structure instead of an en-
semble average as captured by cryo-EM. An attempt to address
the latter is presented in the Supplemental Data (see Simulated
Maps Generated from an Ensemble of Structures), where a pro-
tein structure is fitted into maps created from an ensemble of
structures obtained from equilibrium MD simulations. For these
tests, the fluctuation of atomic positions observed in MDFF
reproduce reasonably well the fluctuations on the target map,
especially for resolutions in the range of 10–15 A.
Example Application: The E. coli Ribosome
The ribosome, a complex macromolecular machine responsi-
ble for protein synthesis in all cells, is one of the biological
678 Structure 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights re
systems for which cryo-EM has provided much insight to
date (Frank, 2003). The ribosome undergoes several confor-
mational changes and binds a number of cofactors throughout
the process of protein synthesis. Different functional states
have been extensively imaged by cryo-EM at ever-increasing
resolution (Frank and Spahn, 2006). The ribosome has driven
the development of methods to obtain quasi-atomic structures
by combining X-ray crystallographic structures with cryo-EM
maps (e.g., Wriggers et al., 2000; Gao et al., 2003; Tama
et al., 2004; Mitra et al., 2005, 2006; for a review, see Mitra
and Frank, 2006).
We present the ribosome as an application of MDFF, using
EM maps corresponding to two functional states, namely, the
E. coli ribosome in complex with the ternary complex EF-Tu$
aminoacyl-tRNA$GDP stalled by the antibiotic kirromycin (70S-
fMet-tRNAfMet-Phe-tRNAPhe$EF-Tu$GDP$kir) at resolutions of
9 A (Valle et al., 2003) and 6.7 A (J. LeBaron, R.A. Grassucci,
T. Shaikh, W. Baxter, J. Sengupta, and J.F., unpublished data),
and a ribosome with an accommodated A-site tRNA at 9 A res-
olution (Valle et al., 2003). The first functional state corresponds
to the initial selection of the ternary complex (TC) in the elonga-
tion cycle, after which EF-Tu leaves the ribosome and, subse-
quently, the peptide bond is formed, resulting in the second
functional state, with a deacylated tRNA occupying the P site
and an accommodated fMet-Phe-tRNAPhe in the A site
(70S-tRNAPhe-MF-tRNAPhe). The atomic model of the ribosome
served
Structure
Molecular Dynamics Flexible Fitting
used in this section is described in the Supplemental Data (see
Atomic Model of the E. coli Ribosome).
The flexible fitting was performed following a multistep proto-
col: (1) After rigid-body docking, the 30S and 50S subunits were
flexibly fitted, using x = 0.3 kcal/mol, km,RNA = 200 kcal
mol�1 rad�2 or 200 kcal mol�1 A�2 for angles and distances,
respectively, and km;protein = 400 kcal mol�1 rad�2. In addition
to the secondary structure restraints, the f and c angles of
the rest of the amino acid residues were restrained with
km;protein = 200 kcal mol�1 rad�2. (2) The potential corresponding
to the 5S, 16S, and 23S rRNAs was deleted, and the atoms in
these chains were restrained to their current positions (positional
restraints) with a relatively stiff force constant of 10 kcal mol�1
A�2, effectively fixing them. This allowed the fitting of ribosomal
proteins to improve, since the potential energy minima corre-
sponding to the ribosomal RNA were removed from the simula-
tion. (3) The harmonic restraints applied to the ribosomal pro-
teins were relaxed to 200 kcal mol�1 rad�2, restraining only
residues in helices and b sheets. (4) The remaining ligands,
namely EF-Tu, tRNAs, and mRNA, were introduced using rigid-
body docking. For this step, the original EM potential (before
RNA deletion) was used, all ribosomal proteins were positionally
restrained, and the positional restraints on the rRNAs were lifted.
The same secondary structure restraints to proteins and RNAs
used in the previous step were preserved and also applied to
the recently introduced ligands. In addition, equivalent RNA re-
straints were imposed to enforce codon-anticodon interactions
between the A-site mRNA codon and the tRNA. During this last
step, force scaling was increased to x = 1.0 kcal/mol. Conver-
gence times and cross-correlation coefficients for each step
are presented for all maps in the Supplemental Data (see Com-
parison between Maps at Different Resolutions). A movie of the
fitting into the 6.7 A map illustrating the multistep protocol can
be found in the Supplemental Data (see Movie S3).
The MDFF method applied to different ribosome cryo-EM
maps yielded quasi-atomic models that closely fit the EM densi-
ties; indeed, the cross-correlation coefficients between the
maps and the fitted structures are significantly higher than those
obtained from rigid-body docking (local correlations with
a threshold of 0.2 s are given in parenthesis): 0.913 (0.764) ver-
sus 0.858 (0.632) (TC-bound ribosome at 6.7 A), 0.919 (0.739)
versus 0.835 (0.503) (TC-bound ribosome at 9.0 A), and 0.878
(0.735) versus 0.756 (0.513) (ribosome with accommodated
A-site tRNA at 9.0 A). Selected regions for which conformational
changes have been previously characterized are presented in
Figure 4. It can be seen that distinct structural elements such
as RNA and protein helices fit well into their corresponding
densities, despite internal restraints imposed to avoid structural
distortions. Local cross-correlation coefficients of different ele-
ments are presented in the Supplemental Data (see Local
Cross-Correlation Coefficient Map).
An overview of the fitting into the 6.7 A map of the TC-bound
ribosome is depicted in Figure 4A, along with a detailed view
of the decoding center. Figure 4B shows the X-ray structure of
tRNA (crystallized in complex with EF-Tu), a fitted structure,
and the same crystal structure fitted manually in a previous study
(Valle et al., 2003). It can be seen that the conformation of the an-
ticodon loop (ACL) of the A/T-site tRNA is significantly different
from the one adopted in the free TC. Interestingly, our fitted
Structur
structure is very similar to the previously proposed one; how-
ever, the previous work assumed that the ACL of the A/T-site
tRNA adopts the same conformation as that of the free ternary
complex, and thus a model of the structure was built by interpo-
lating coordinates between two manual fittings of the same
crystal structure (Valle et al., 2003). With the MDFF method, we
obtained the conformational change that the ACL undergoes
when the TC binds to the ribosome without any assumptions,
the fitting being driven only by the EM data. The structure of
the ACL of the A/T-site tRNA obtained from our fitting has the
same conformation as the ACL of the A-site tRNA observed by
Selmer et al. (2006), as shown in Figure 4C. A comparison be-
tween the fittings into cryo-EM maps of the TC-bound ribosome
at different resolutions (6.7 A and 9.0 A) is presented in the
Supplemental Data (see Comparison between Maps at Different
Resolutions).
Binding of the TC to the ribosome induces a conformational
change in the GTPase-associated center (GAC) (Valle et al.,
2003). Figure 4D presents a comparison of the GAC conforma-
tion in the TC-bound ribosome and the ribosome in complex
with an accommodated A-site tRNA. In the first conformation
(closed), the GAC approaches the 50S to interact with the TC;
when EF-Tu leaves the ribosome, the second conformation
(open) arises in which the GAC lobe moves back to its original
position. One can see that rigid-body docking of the crystal
structure to the ribosomal cryo-EM map with an accommodated
A-site tRNA shows a good fit for the GAC, revealing that the crys-
tal structure captures this conformation. Flexible fitting obtains
a closer match to the EM map for this state and reveals the
closed conformation of the GAC and TC in the TC-bound ribo-
some. The details of the atomic structures obtained from the
6.7 A map will be discussed elsewhere (J. Sengupta, E.V.,
L.G.T., J. LeBaron, W.T. Baxter, T. Shaikh, R.A. Grassucci,
P. Nissen, M. Ehrenberg, K.S., and J.F., unpublished data).
Even at subnanometer resolution that permits the identifica-
tion of secondary structure elements, some regions are not
well defined in an EM map. For example, the switch regions of
EF-Tu in the 6.7 A TC-bound ribosomal EM map are not re-
solved, presumably due to their high flexibility. Though informa-
tion about their structure is not directly available in the EM map,
MD simulations can be performed in the presence of the EM po-
tential to assess the feasibility of different conformations of the
switches: an unfeasible conformation will either change during
simulation, or alter the quality of the fit of neighboring domains.
The conformational dynamics of the interaction of EF-Tu with
the ribosome can be deduced from the computational studies,
even though a crystal structure of a ribosome-bound EF-Tu is
not yet available, and density for some key elements governing
the interaction is missing in the EM map (J. Sengupta, E.V.,
L.G.T., J. LeBaron, W.T. Baxter, T. Shaikh, R.A. Grassucci,
P. Nissen, M. Ehrenberg, K.S., and J.F., unpublished data).
DISCUSSION
We have developed a novel method, MDFF, for combining
atomic structures and EM maps to reveal atomic details of mac-
romolecular complexes in functional states. High-resolution
structures of complexes imaged by cryo-EM permit a better in-
terpretation of the data, e.g., by characterizing the flexibility of
e 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 679
Structure
Molecular Dynamics Flexible Fitting
the complex, identifying key interactions between its composing
elements, or locating bound cofactors. The MDFF method takes
advantage of the impressive advances both in X-ray crystallog-
raphy and cryo-EM, by using MD simulations that incorporate
EM data through a potential driving an atomic structure into
a conformation corresponding to an EM map. The method has
several characteristics that bring together the best features of
previously developed methods: (1) MDFF avoids the use of
reduced representations which necessarily discard some of the
information contained in the crystal structure or the EM map.
(2) MDFF considers information contained in the map through
a potential, such that the fitting is performed locally, i.e., inde-
pendently of other regions of a molecule. (3) MDFF uses global
measures of the fit only to assess convergence and not to drive
the fit. Methods that rely on global measures to obtain a good fit
become less efficient as the size of the system increases. (4)
MDFF can be used to fit both protein and nucleic acids, as well
Figure 4. Fitting into the TC-Bound Ribo-
some Cryo-EM Map at 6.7 A Resolution by
Means of MDFF
(A) Overview of the all-atom ribosome structure fit-
ted into the 6.7 A map, with a close view into the
decoding center (inset).
(B) Conformation of tRNA in the A/T site. The crys-
tal structure from the free TC used as a starting
point for the fitting (PDB code: 1OB2; unpublished
data) is shown in red; the A/T tRNA model ob-
tained by applying the MDFF method to the 6.7 A
map is shown in blue; the A/T tRNA model previ-
ously obtained using a 9.0 A map constructed by
interpolating two manual fittings of tRNA (PDB
code: 1OB2) is shown in green (Valle et al., 2003).
(C) Conformation of tRNA in the A/T site (blue)
compared to a partial crystal structure of the
A-site tRNA (Selmer et al., 2006) (red). The crystal
structure from the free TC used as a starting point
for the fitting (PDB code: 1OB2; unpublished data)
is shown on the left; the A/T tRNA model obtained
by applying the MDFF method to the 6.7 A map is
shown on the right.
(D) Conformational dynamics of the GTPase-asso-
ciated center. Shown are differences in the confor-
mation of the GTPase-associated center between
the TC-bound ribosome (EM map at 6.7-A resolu-
tion, top), and the accommodated ribosome (EM
map at 9 A resolution, bottom). Rigid-body docked
structures into the corresponding maps, used as
initial coordinates for flexible fitting, are shown
on the left; flexibly fitted structures are shown on
the right.
as systems composed of both. (5) MDFF
can fit parts of the complex indepen-
dently when complete atomic structures
are not available. (6) MDFF does not re-
quire user input to divide a molecule into
pieces to flexibly fit them into the map;
rather, the flexibility is indigenous to the
molecular structure, with additional re-
straints dictated by the secondary struc-
ture. (7) MDFF follows multistep protocols
that permit adjusting the method to face various challenges; e.g.,
in the case of systems composed of protein and nucleic acids,
fitting can be performed on nucleic acids first and the protein
component second. (8) MDFF ensures stereochemical correct-
ness during the fitting process, obviating the need for post-fitting
refinement, which often results in deviations from the EM map. In
fact, the structures obtained by MDFF can be used as initial co-
ordinates for further simulation studies, in particular, for an equil-
ibration testing the stability of the model arrived at. (9) MDFF
uses restraints to preserve secondary structure elements and
other structural features in order to prevent overfitting; in this re-
spect it bears some similarity to real-space refinement (Chap-
man, 1995), but MDFF is more automated and more adaptive.
(10) MDFF can represent the structural variability present in the
experimental map by providing a representative set of fitted
structures instead of a single one. (11) MDFF can be extended
to take advantage of other enhanced-sampling techniques
680 Structure 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved
Structure
Molecular Dynamics Flexible Fitting
such as the use of elastic network models (Tama et al., 2004;
Schroder et al., 2007).
A natural concern about flexible fitting methods is overfitting.
We have shown that the harmonic restraints proposed are
enough to prevent overfitting into noise-free maps. However,
the degree of overfitting into experimental EM maps prevented
by applying the restraints presented here cannot be evaluated
at this time, and thus users are discouraged from softening the
tight restraints suggested in this paper. The choice of restraints
in MDFF might be improved further, e.g., through incorporation
of restraints based on rigidity analysis (Jacobs et al., 2001; Jolley
et al., 2008). A limitation intrinsic to our method is that rotation of
structural elements are difficult to capture; this may be ad-
dressed, e.g., by enhancing the lowest frequency normal modes
in the simulation (Zhang et al., 2003) or by refining with MDFF
models generated with a flexible fitting method based on normal
modes (Tama et al., 2004; Suhre et al., 2006). Naturally, with the
current restraints it is not possible to capture conformational
changes that involve unfolding of secondary structure elements.
Even though the fitting in MDFF is performed locally, proteins
that interact with nucleic acids should not be fitted in the
absence of the latter, since they might be attracted to the higher
nucleic acid density. An interesting alternative involves the use of
local, but not global, cross-correlation maps to define UEM.
Naturally, MDFF results cannot be better than the EM data
used permit. Any artifact in the molecular density reported in
the EM map can be propagated to the fitted structure. The quan-
titative use of the density map requires high-quality data collec-
tion and efficient 3D reconstruction algorithms, as extensively
discussed in Frank (2006). The fitting and the interpretation of
the resulting structures must be done taking into account factors
that prevent the 3D reconstruction from accurately representing
the molecular density. An additional concern that the MDFF
technique might raise is computational cost. Indeed, the neces-
sary calculations are extensive, akin to other available flexible-
fitting methods (Schroder et al., 2007; Wriggers and Birmanns,
2001). However, with the prospect of automated cryo-EM data
eventually being able to match the speed of throughput achieved
by other structural methods (Zhu et al., 2001), the advantages of
not requiring ad hoc user input and of incorporating as much of
information from the original data as possible, together with ex-
pected increases in computer power, will make MDFF a feasible
and attractive tool for obtaining atomic structures from the
wealth of EM data. Moreover, by using NAMD, the computa-
tional cost of the MDFF method scales linearly with system
size, permitting the application of MDFF to large macromolecular
complexes.
The success of the MDFF method is evident from the quality of
the high-resolution structures obtained for cryo-EM maps of ri-
bosomal complexes. The ribosome represents one of the great-
est challenges to fitting methods due to its sheer size, its lack of
symmetry, and its mixed composition of protein and RNA. We
have recently fitted atomic structures to several ribosomal
cryo-EM maps to study the conformational changes that take
place during the decoding process. (K.M., L.G.T., E.V., A. Zavia-
lov, M. Ehrenberg, K.S., and J.F., unpublished data; J. Sengupta,
E.V., L.G.T., J. LeBaron, W.T. Baxter, T. Shaikh, R.A. Grassucci,
P. Nissen, M. Ehrenberg, K.S., and J.F., unpublished data). Typ-
ical global cross-correlation coefficients obtained improve from
Structure
�0.8 after rigid-body docking, to �0.9 after completion of the
flexible fitting.
In recent years, it has become evident that cellular functions
are carried out by assemblies of interacting macromolecules
(Alberts, 1998), many of them existing only transiently in the
cell. In order to provide a comprehensive description of such
complexes, spanning the atomic and the system level, data ob-
tained from various structural techniques must be combined into
high-resolution structures with the aid of theoretical approaches
(Sali et al., 2003; Alber et al., 2007). MD is a method of choice,
being increasingly used to refine macromolecular structures,
and is an established tool for studying structural dynamics of
large biomolecules. The conceptual grounds of the methodology
presented here can easily be extended to other sources of struc-
tural data by including them in MD simulations of atomic or
coarse-grained structures (Shih et al., 2007; Arkhipov et al.,
2006) as external potentials that merge several levels of descrip-
tion into high-resolution structures.
As structural methods become more prolific, automated soft-
ware capable of interpreting intermediate-resolution structures
at the atomic level is becoming crucial; indeed, it seems likely
that in years to come this type of approach will yield the main,
and perhaps only, source of atomic structures for large macro-
molecular complexes in functional conformations. The software
should be widely available and should not require very detailed
technical expertise or ad hoc input, but rather should be easy
to use and general. These requirements are met by the MDFF
method. The method is currently implemented in the molecular
dynamics software package NAMD (Phillips et al., 2005), and
the automated setup and analysis of the simulations is done
through the molecular visualization software package VMD
(Humphrey et al., 1996).
SUPPLEMENTAL DATA
Supplemental Data include an overview of MD simulations and 3D EM recon-
structions; several additional validation cases for MDFF, including density
maps generated from an MD simulation; a description of the atomic model
of the E. coli ribosome used in the current work; an analysis of the effect of res-
olution on the fitting into experimental cryo-EM maps; a local cross-correlation
coefficient map for a fitted ribosome structure; and three movies illustrating the
MDFF method. Supplemental Data can be found with this article online at
http://www.structure.org/cgi/content/full/16/5/673/DC1/.
ACKNOWLEDGMENTS
The authors would like to thank David Wells, Aleksei Aksimientiev, and Jim
Phillips for help with the implementation of the MDFF method in NAMD; Jordi
Cohen for stimulating discussions; and Emma Falck for contributing to initial
stages of this project. This work was supported by HHMI (J.F.), the Burroughs
Wellcome Fund (K.M.), and grants NIH P41-RR05969 (K.S.), NIH P41-
RR01219, NIH R37-GM29169, and NIH R01-GM55440 (J.F.). Computer time
was provided through LRAC grant MCA93S028 (K.S.).
Received: January 16, 2008
Revised: March 3, 2008
Accepted: March 22, 2008
Published: May 6, 2008
REFERENCES
Alber, F., Dokudovskaya, S., Veenhoff, L.M., Zhang, W., Kipper, J., Devos, D.,
Suprapto, A., Karni-Schmidt, O., Williams, R., Chait, B.T., et al. (2007). Deter-
mining the architectures of macromolecular assemblies. Nature 450, 683–694.
16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 681
Structure
Molecular Dynamics Flexible Fitting
Alberts, B. (1998). The cell as a collection of protein machines – preparing the
next generation of biologists. Cell 92, 291–294.
Arkhipov, A., Freddolino, P.L., and Schulten, K. (2006). Stability and dynamics
of virus capsids described by coarse-grained modeling. Structure 14,
1767–1777.
Brunger, A.T., Brooks, C.L., III, and Karplus, M. (1984). Stochastic boundary
conditions for molecular dynamics simulations of ST2 water. Chem. Phys.
Lett. 105, 495–498.
Chapman, M.S. (1995). Restrained real-space macromolecular atomic refine-
ment using a new resolution-dependent electron-density function. Acta Crys-
tallogr. A 51, 69–80.
Chen, L.F., Blanc, E., Chapman, M.S., and Taylor, K.A. (2001). Real space re-
finement of acto-myosin structures from sectioned muscle. J. Struct. Biol. 133,
221–232.
Darnault, C., Volbeda, A., Kim, E.J., Legrand, P., Vernede, X., Lindahl, P.A.,
and Fontecilla-Camps, J.C. (2003). Ni-Zn-[Fe-S] and Ni-Ni-[Fe-S] clusters
in closed and open a subunits of acetyl-CoA synthase/carbon monoxide
dehydrogenase. Nat. Struct. Biol. 10, 271–279.
Foloppe, N., and MacKerrell, A.D., Jr. (2000). All-atom empirical force field for
nucleic acids: I. Parameter optimization based on small molecule and con-
densed phase macromolecular target data. J. Comput. Chem. 21, 86–104.
Frank, J. (2002). Single-particle imaging of macromolecules by cryo-electron
microscopy. Annu. Rev. Biophys. Biomol. Struct. 31, 309–319.
Frank, J. (2003). Electron microscopy of functional ribosome complexes.
Biopolymers 68, 223–233.
Frank, J. (2006). Three-Dimensional Electron Microscopy of Macromolecular
Assemblies (New York: Oxford University Press).
Frank, J., and Spahn, C.M.T. (2006). The ribosome and the mechanism of
protein synthesis. Rep. Prog. Phys. 69, 1383–1417.
Frenkel, D., and Smit, B. (2002). Understanding Molecular Simulation From
Algorithms to Applications (California: Academic Press).
Gao, H., Sengupta, J., Valle, M., Korostelev, A., Eswar, N., Stagg, S.M., Van
Roey, P., Agrawal, R.K., Harvey, S.C., Sali, A., et al. (2003). Study of the struc-
tural dynamics of the E. coli 70S ribosome using real space refinement. Cell
113, 789–801.
Humphrey, W., Dalke, A., and Schulten, K. (1996). VMD – Visual Molecular
Dynamics. J. Mol. Graph. 14, 33–38.
Isralewitz, B., Gao, M., and Schulten, K. (2001). Steered molecular dynamics
and mechanical functions of proteins. Curr. Opin. Struct. Biol. 11, 224–230.
Jacobs, D.J., Rader, A.J., Kuhn, L.A., and Thorpe, M.F. (2001). Protein flexibil-
ity predictions using graph theory. Proteins 44, 150–165.
Jolley, C.C., Wells, S.A., Fromme, P., and Thorpe, M.F. (2008). Fitting low-res-
olution cryo-EM maps of proteins using constrained geometric simulations.
Biophys. J. 94, 1613–1621.
Leontis, N.B., and Westhof, E. (1998). Conserved geometrical base-pairing
patters in RNA. Q. Rev. Biophys. 31, 399–455.
Li, W., and Frank, J. (2007). Transfer RNA in the hybrid P/E state: Correlating
molecular dynamics simulations with cryo-EM data. Proc. Natl. Acad. Sci.
USA 104, 16540–16545.
MacKerell, A., Jr., Bashford, D., Bellott, M., Dunbrack, R.L., Jr., Evanseck, J.,
Field, M.J., Fischer, S., Gao, J., Guo, H., Ha, S., et al. (1998). All-atom empirical
potential for molecular modeling and dynamics studies of proteins. J. Phys.
Chem. B 102, 3586–3616.
Mitra, K., and Frank, J. (2006). Ribosome dynamics: insights from atomic
structure modeling into cryo-electron microscopy maps. Annu. Rev. Biophys.
Biomol. Struct. 35, 299–317.
Mitra, K., Schaffitzel, C., Shaikh, T., Tama, F., Jenni, S., Brooks, C.L., Ban, N.,
and Frank, J. (2005). Structure of the E. coli protein-conducting channel bound
to a translating ribosome. Nature 438, 318–324.
Mitra, K., Schaffitzel, C., Fabiola, F., Chapman, M., Ban, N., and Frank, J.
(2006). Elongation arrest by SecM via a cascade of ribosomal RNA rearrange-
ments. Mol. Cell 22, 533–543.
682 Structure 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights re
Phillips, J.C., Braun, R., Wang, W., Gumbart, J., Tajkhorshid, E., Villa, E.,
Chipot, C., Skeel, R.D., Kale, L., and Schulten, K. (2005). Scalable molecular
dynamics with NAMD. J. Comput. Chem. 26, 1781–1802.
Roseman, A.M. (2000). Docking structures of domains into maps from cryo-
electron microscopy using local correlation. Acta Crystallogr. D Biol. Crystal-
logr. 56, 1332–1340.
Rossmann, M.G. (2000). Fitting atomic models into electron-microscopy
maps. Acta Crystallogr. D Biol. Crystallogr. 56, 1341–1349.
Saibil, H.R. (2000). Macromolecular structure determination by cryo-electron
microscopy. Acta Crystallogr. D Biol. Crystallogr. 56, 1215–1222.
Sali, A., Glaeser, R., Earnest, T., and Baumeister, W. (2003). From words to
literature in structural proteomics. Nature 422, 216–225.
Schroder, G.F., Brunger, A.T., and Levitt, M. (2007). Combining efficient con-
formational sampling with a deformable elastic network model facilitates
structure refinement at low resolution. Structure 15, 1630–1641.
Schuwirth, B.S., Borovinskaya, M.A., Hau, C.W., Zhang, W., Vila-Sanjurjo, A.,
Holton, J.M., and Cate, J.H.D. (2005). Structures of the bacterial ribosome at
3.5 A resolution. Science 310, 827–834.
Selmer, M., Dunham, C.M., Murphy, F.V., IV, Weixlbaumer, A., Petry, S.,
Kelley, A.C., Weir, J.R., and Ramakrishnan, V. (2006). Structure of the 70S
ribosome complexed with mRNA and tRNA. Science 313, 1935–1942.
Shih, A.Y., Freddolino, P.L., Arkhipov, A., and Schulten, K. (2007). Assembly of
lipoprotein particles revealed by coarse-grained molecular dynamics simula-
tions. J. Struct. Biol. 157, 579–592.
Sotomayor, M., and Schulten, K. (2007). Single-molecule experiments in vitro
and in silico. Science 316, 1144–1148.
Stewart, P.L., Fuller, S.D., and Burnett, R.M. (1993). Difference imaging of
adenovirus: Bridging the resolution gap between X-ray crystallography and
electron microscopy. EMBO J. 12, 2589–2599.
Suhre, K., Navaza, J., and Sanejouand, Y.H. (2006). NORMA: a tool for flexible
fitting of high-resolution protein structures into low-resolution electron-
microscopy-derived density maps. Acta Crystallogr. D Biol. Crystallogr. 62,
1098–1100.
Tama, F., Miyashita, O., and Brooks, C.L., III. (2004). Normal mode based
flexible fitting of high-resolution structure into low-resolution experimental
data from cryo-EM. J. Struct. Biol. 147, 315–326.
Topf, M., Baker, M.L., Marc-Renom, M.A., Chiu, W., and Sali, A. (2006). Refine-
ment of protein structures by iterative comparative modeling and cryoEM
density fitting. J. Mol. Biol. 357, 1655–1668.
Topf, M., Lasker, K., Webb, B., Wolfson, H., Chiu, W., and Sali, A. (2008).
Protein structure fitting and refinement guided by cryo-EM density. Structure
16, 295–307.
Valle, M., Zavialov, A., Li, W., Stagg, S.M., Sengupta, J., Nielsen, R.C., Nissen,
P., Harvey, S.C., Ehrenberg, M., and Frank, J. (2003). Incorporation of amino-
acyl-tRNA into the ribosome as seen by cryo-electron microscopy. Nat. Struct.
Biol. 10, 899–906.
Velazquez-Muriel, J.A., Valle, M., Santamarıa-Pang, A., Kakadiaris, I.A., and
Carazo, J.M. (2006). Flexible fitting in 3D-EM guided by the structural variability
of protein superfamilies. Structure 14, 1115–1126.
Volkmann, N., Hanein, D., Ouyang, G., Trybus, K.M., DeRosier, D.J., and
Lowey, S. (2000). Evidence for cleft closure in actomyosin upon ADP release.
Nat. Struct. Biol. 7, 1147–1155.
Wells, D.B., Abramkina, V., and Aksimentiev, A. (2007). Exploring transmem-
brane transport through a-hemolysin with grid-steered molecular dynamics.
J. Chem. Phys. 127, 125101–125110.
Wriggers, W., and Birmanns, S. (2001). Using Situs for flexible and rigid-body
fitting of multiresolution single-molecule data. J. Struct. Biol. 133, 193–202.
Wriggers, W., and Chacon, P. (2001). Modeling tricks and fitting techniques for
multiresolution structures. Structure 9, 779–788.
Wriggers, W., Milligan, R.A., and McCammon, J.A. (1999). Situs: A package for
docking crystal structures into low-resolution maps from electron microscopy.
J. Struct. Biol. 125, 185–195.
served
Structure
Molecular Dynamics Flexible Fitting
Wriggers, W., Agrawal, R.K., Drew, D.L., McCammon, A., and Frank, J. (2000).
Domain motions of EF-G bound to the 70S ribosome: Insights from a hand-
shaking between multi-resolution structures. Biophys. J. 79, 1670–1678.
Yang, H., Jossinet, F., Leontis, N., Chen, L., Westbrook, J., Berman, H., and
Westhof, E. (2003). Tools for the automatic identification and classification of
RNA base pairs. Nucleic Acids Res. 31, 3450–3460.
Structur
Zhang, Z., Shi, Y., and Liu, H. (2003). Molecular dynamics simulations of
peptides and proteins with amplified collective motions. Biophys. J. 84,
3583–3593.
Zhu, Y., Carrangher, B., Kriegman, D.J., Milligan, R.A., and Potter, C.S. (2001).
Automated identification of filaments in cryoelectron microscopy images.
J. Struct. Biol. 135, 302–312.
e 16, 673–683, May 2008 ª2008 Elsevier Ltd All rights reserved 683